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<ri:Resource created="2024-06-26T07:23:29Z" status="active" updated="2025-05-19T09:50:00Z" version="1.2" xmlns:ri="http://www.ivoa.net/xml/RegistryInterface/v1.0" xmlns:vr="http://www.ivoa.net/xml/VOResource/v1.0" xmlns:vs="http://www.ivoa.net/xml/VODataService/v1.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.ivoa.net/xml/VOResource/v1.0 http://vo.ari.uni-heidelberg.de/docs/schemata/VOResource.xsd http://www.ivoa.net/xml/VODataService/v1.1 http://vo.ari.uni-heidelberg.de/docs/schemata/VODataService.xsd" xsi:type="vs:CatalogService"><title>Asteroids spin orientation and phase function</title><shortName>J/A+A/687/A38</shortName><identifier>ivo://CDS.VizieR/J/A+A/687/A38</identifier><altIdentifier>doi:10.26093/cds/vizier.36870038</altIdentifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Carry B.</name></creator><creator><name>Peloton J.</name></creator><creator><name>Le Montagner R.</name></creator><creator><name>Mahlke M.</name></creator><creator><name>Berthier J.</name></creator><date role="Updated">2024-11-21T20:02:18Z</date><date role="Created">2024-06-26T07:23:29Z</date><contact><name>CDS support team</name><address>CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France</address><email>cds-question@unistra.fr</email></contact></curation><content><subject>solar-system</subject><subject>asteroids</subject><subject>photometry</subject><subject>visible-astronomy</subject><subject>astronomical-models</subject><description>Large sky surveys provide numerous non-targeted observations of small bodies of the Solar System. The upcoming Legacy Survey of Space and Time (LSST) of the Vera C. Rubin observatory will be the largest source of small body photometry in the next decade. With non-coordinated epochs of observation, colors, and therefore taxonomy and composition, can only be computed by comparing absolute magnitudes obtained in each filter by solving the phase function (evolution of brightness of the small body against the solar phase angle). Current models in use in the community (HG, HG12*, HG1G2) however fail to reproduce the long-term photometry of many targets due to the change in aspect angle between apparitions. We aim at deriving a generic yet simple phase function model accounting for the variable geometry of the small bodies over multiple apparitions. As a spinoff of the HG1 G2 model, we propose the sHG1 G2 phase function model in which we introduce a term describing the brightness changes due to spin orientation and polar oblateness. We apply this new model to 13245908 observations of 122675 SSOs. These observations were acquired in the g and r filters with the Zwicky Transient Facility between 2019/11/01 and 2023/12/01. We retrieve them and implement the new sHG1 G2 model in Fink, a broker of alerts designed for the LSST. The sHG1 G2 model leads to smaller residuals than other phase function models, providing a better description of the photometry of asteroids. We determine the absolute magnitude H and phase function coefficients (G1, G2) in each filter, the spin orientation ({alpha}_0_ , {delta}_0_), and the polar-to-equatorial oblateness R for 95593 Solar System Objects (SSOs), which constitutes about a tenfold increase in the number of characterized objects compared to current census. The application of the sHG1 G2 model on ZTF alert data using the FINK broker shows that the model is appropriate to extract physical properties of asteroids from multi-band and sparse photometry, such as the forthcoming LSST survey.</description><source format="bibcode">2024A&amp;A...687A..38C</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/687/A38</referenceURL><type>Catalog</type><contentLevel>Research</contentLevel><relationship><relationshipType>IsServedBy</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/TAP">TAP VizieR generic service</relatedResource></relationship><relationship><relationshipType>related-to</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/B/astorb">B/astorb : Orbits of Minor Planets (Bowell+, 2014-)</relatedResource></relationship></content><rights>https://cds.unistra.fr/vizier-org/licences_vizier.html</rights><capability><interface xsi:type="vr:WebBrowser"><accessURL use="full">https://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/687/A38</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/687/A38</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/687/A38</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/687/A38</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/687/A38</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/687/A38</mirrorURL><queryType>GET</queryType><resultType>text/xml+votable</resultType></interface></capability><capability standardID="ivo://ivoa.net/std/TAP#aux"><interface xsi:type="vs:ParamHTTP" role="std"><accessURL use="base">https://tapvizier.cds.unistra.fr/TAPVizieR/tap</accessURL></interface></capability><coverage><footprint ivo-id="ivo://ivoa.net/std/moc"/><waveband>Optical</waveband></coverage><tableset><schema><name>default</name><table><name>J/A+A/687/A38/catalog</name><description>FINK SSOFT (ZTF photometry, FINK broker)</description><column><name>HG1G2-status</name><description>Fit status of HG1G2 model (HG1G2_status)</description><ucd>meta.code</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>recno</name><description>Record number assigned by the VizieR team. Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>SHG1G2-rms</name><description>? RMS residuals of sHG1G2 model (SHG1G2_rms)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SSOnumber</name><description>? Official IAU number (sso_number)</description><ucd>meta.id</ucd><dataType xsi:type="vs:VOTableType">int</dataType><flag>nullable</flag></column><column><name>SSOname</name><description>Official IAU designation (sso_name)</description><ucd>meta.id;meta.main</ucd><dataType xsi:type="vs:VOTableType" arraysize="17*">char</dataType></column><column><name>Nobs</name><description>? Total number of observations (n_obs)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">int</dataType><flag>nullable</flag></column><column><name>Nobs-g</name><description>? Number of observations in g filter (n_obs_g)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">int</dataType><flag>nullable</flag></column><column><name>Nobs-r</name><description>? Number of observations in r filter (n_obs_r)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">int</dataType><flag>nullable</flag></column><column><name>Minphase</name><description>? Minimum phase angle of observations (min_phase)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Minphase-g</name><description>? Minimum phase angle of observations in g filter (min_phase_g)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Minphase-r</name><description>? Minimum phase angle of observations in r filter (min_phase_r)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Maxphase</name><description>? Maximum phase angle of observations (max_phase)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Maxphase-g</name><description>? Maximum phase angle of observations in g filter (max_phase_g)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Maxphase-r</name><description>? Maximum phase angle of observations in r filter (max_phase_r)</description><ucd>src.orbital</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Ndays</name><description>? Number of days covered by observations (n_days)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Ndays-g</name><description>? Number of days covered by observations in g filter (n_days_g)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>Ndays-r</name><description>? Number of days covered by observations in r filter (n_days_r)</description><ucd>meta.number</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-H-g</name><description>? Absolute magnitude H in HG model in g filter (HG_H_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG-H-g</name><description>? Uncertainty on the absolute magnitude H in HG model in g filter (HG_dH_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-G-g</name><description>? Phase slope G in HG model in g filter (HG_G_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG-G-g</name><description>? Uncertainty on phase slope G in HG model in g filter (HG_dG_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-H-r</name><description>? Absolute magnitude H in HG model in r filter (HG_H_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG-H-r</name><description>? Uncertainty on the absolute magnitude H in HG model in r filter (HG_dH_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-G-r</name><description>? Phase slope G in HG model in r filter (HG_G_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG-G-r</name><description>? Uncertainty on phase slope G in HG model in r filter (HG_dG_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-rms</name><description>? RMS residuals of HG model (HG_rms)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-rms-g</name><description>? RMS residuals of HG model in g filter (HG_rms_g)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-rms-r</name><description>? RMS residuals of HG model in r filter (HG_rms_r)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG-chi2red</name><description>? Chi-square of HG model (HG_chi2red)</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG-status</name><description>Fit status of HG model (HG_status)</description><ucd>meta.code</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>HG-fit</name><description>Quality code of the fit of HG model (HG_fit)</description><ucd>meta.code.qual;stat.fit.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>HG1G2-H-g</name><description>? Absolute magnitude H in HG1G2 model in g filter (HG1G2_H_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-H-g</name><description>? Uncertainty on the absolute magnitude H in HG1G2 model in g filter (HG1G2_dH_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-G1-g</name><description>? Phase slope G1 in HG1G2 model in g filter (HG1G2_G1_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-G1-g</name><description>? Uncertainty on phase slope G1 in HG1G2 model in g filter (HG1G2_dG1_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-G2-g</name><description>? Phase slope G2 in HG1G2 model in g filter (HG1G2_G2_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-G2-g</name><description>? Uncertainty on phase slope G2 in HG1G2 model in g filter (HG1G2_dG2_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-H-r</name><description>? Absolute magnitude H in HG1G2 model in r filter (HG1G2_H_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-H-r</name><description>? Uncertainty on the absolute magnitude H in HG1G2 model in g filter (HG1G2_dH_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-G1-r</name><description>? Phase slope G1 in HG1G2 model in r filter (HG1G2_G1_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-G1-r</name><description>? Uncertainty on phase slope G1 in HG1G2 model in r filter (HG1G2_dG1_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-G2-r</name><description>? Phase slope G2 in HG1G2 model in r filter (HG1G2_G2_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_HG1G2-G2-r</name><description>? Uncertainty on phase slope G2 in HG1G2 model in r filter (HG1G2_dG2_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-rms</name><description>? RMS residuals of HG1G2 model (HG1G2_rms)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG1G2-rms-g</name><description>? RMS residuals of HG1G2 model in g filter (HG1G2_rms_g)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG1G2-rms-r</name><description>? RMS residuals of HG1G2 model in r filter (HG1G2_rms_r)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>HG1G2-chi2red</name><description>? Chi-square of HG1G2 model (HG1G2_chi2red)</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>HG1G2-fit</name><description>Quality code of the fit of HG1G2 model (HG1G2_fit)</description><ucd>meta.code.qual;stat.fit.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>SHG1G2-H-g</name><description>? Absolute magnitude H in sHG1G2 model in g filter (SHG1G2_H_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-H-g</name><description>? Uncertainty on absolute magnitude H in sHG1G2 model in g filter (SHG1G2_dH_g)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>sHG1G2-status</name><description>Fit status of sHG1G2 model (sHG1G2_status)</description><ucd>meta.code</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>SHG1G2-G1-g</name><description>? Phase slope G1 in sHG1G2 model in g filter (SHG1G2_G1_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-G1-g</name><description>? Uncertainty on phase slope G1 in sHG1G2 model in g filter (SHG1G2_dG1_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-G2-g</name><description>? Phase slope G2 in sHG1G2 model in g filter (SHG1G2_G2_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-G2-g</name><description>? Uncertainty on phase slope G2 in sHG1G2 model in g filter (SHG1G2_dG2_g)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-H-r</name><description>? Absolute magnitude H in sHG1G2 model in r filter (SHG1G2_H_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-H-r</name><description>? Uncertainty on absolute magnitude H in sHG1G2 model in r filter (SHG1G2_dH_r)</description><unit>mag</unit><ucd>phys.magAbs</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-G1-r</name><description>? Phase slope G1 in sHG1G2 model in r filter (SHG1G2_G1_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-G1-r</name><description>? Uncertainty on phase slope G1 in sHG1G2 model in r filter (SHG1G2_dG1_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-G2-r</name><description>? Phase slope G2 in sHG1G2 model in r filter (SHG1G2_G2_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-G2-r</name><description>? Uncertainty on phase slope G2 in sHG1G2 model in r filter (SHG1G2_dG2_r)</description><ucd>meta.cryptic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-R</name><description>? Oblateness (SHG1G2_R)</description><ucd>phys.size;arith.ratio</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>e_SHG1G2-R</name><description>? Uncertainty on oblateness (SHG1G2_dR)</description><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2-alpha0</name><description>? Right Ascension of the spin vector (SHG1G2_alpha0)</description><unit>deg</unit><ucd>pos.eq.ra</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2-delta0</name><description>? 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Uncertainty on the Declination of the spin vector (SHG1G2_ddelta0)</description><unit>deg</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>SHG1G2-obliquity</name><description>? Obliquity of the target (SHG1G2_obliquity)</description><unit>deg</unit><ucd>src.orbital.inclination</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2mincoslambda</name><description>? Minimum cosine of the aspect angle Lambda (SHG1G2_min_cos_lambda)</description><ucd>src.orbital.inclination</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2meancoslambda</name><description>? Mean cosine of the aspect angle Lambda (SHG1G2_mean_cos_lambda)</description><ucd>src.orbital.inclination</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2maxcoslambda</name><description>? Maximum cosine of the aspect angle Lambda (SHG1G2_max_cos_lambda)</description><ucd>src.orbital.inclination</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2-rms-g</name><description>? RMS residuals of sHG1G2 model in g filter (SHG1G2_rms_g)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>SHG1G2-rms-r</name><description>? RMS residuals of sHG1G2 model in g filter (SHG1G2_rms_r)</description><ucd>stat.fit.residual</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>sHG1G2-chi2red</name><description>? Chi-square of sHG1G2 model (sHG1G2_chi2red)</description><ucd>stat.fit.chi2</ucd><dataType xsi:type="vs:VOTableType">float</dataType><flag>nullable</flag></column><column><name>sHG1G2-fit</name><description>Quality code of the fit of sHG1G2 model (sHG1G2_fit)</description><ucd>meta.code.qual;stat.fit.param;meta.modelled</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column></table></schema></tableset></ri:Resource>